Zhi Huimin, Wei Jumei, Liu Yanhong, Ding Shuai, Owens David H
School of Electrical Engineering, Zhengzhou University, Zhengzhou, Henan, 450001, China.
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan, 450001, China.
ISA Trans. 2023 Nov;142:573-584. doi: 10.1016/j.isatra.2023.07.011. Epub 2023 Jul 13.
The conventional tracking control of mechanical systems is generally based on the stabilization of error dynamics and most of the results can only guarantee asymptotic tracking of the desired trajectories. Since error dynamics are generally time-varying, it is very difficult to find appropriate Lyapunov functions or control Lyapunov functions to complete stability analysis and controller design. To address this limitation, the novel constructive exponential tracking control method is proposed to mechanical systems by utilizing the Hamiltonian realization and contraction analysis in this paper. Firstly, based on the Hamiltonian realization and use the structural characteristics of port-Hamiltonian systems, the exponential tracking controllers are constructed for fully actuated and under-actuated mechanical systems by combining the pre-feedback with feedback control. The proposed tracking control strategies can be used to discuss fully actuated and under-actuated mechanical systems in a unified framework. Then the exponential decay-rate of tracking controllers and procedure for selecting control parameters for fully actuated and under-actuated mechanical systems are given. Finally, comparative simulations and experiments are carried out to illustrate the effectiveness and robustness of the proposed control strategy.
机械系统的传统跟踪控制通常基于误差动态的稳定，并且大多数结果只能保证对期望轨迹的渐近跟踪。由于误差动态通常是时变的，因此很难找到合适的李雅普诺夫函数或控制李雅普诺夫函数来完成稳定性分析和控制器设计。为了解决这一局限性，本文利用哈密顿实现和收缩分析，针对机械系统提出了新颖的构造性指数跟踪控制方法。首先，基于哈密顿实现并利用端口哈密顿系统的结构特性，通过将前馈与反馈控制相结合，为完全驱动和欠驱动机械系统构造指数跟踪控制器。所提出的跟踪控制策略可用于在统一框架内讨论完全驱动和欠驱动机械系统。然后给出了完全驱动和欠驱动机械系统跟踪控制器的指数衰减率以及控制参数的选择过程。最后，通过对比仿真和实验来说明所提出控制策略的有效性和鲁棒性。
